Normal-Mode Parameters of Microstrip Coupled Lines of Unequal Width (Short Paper)

Empirical relations for the capacitive and inductive coupling coefficients have been used to compute normal-mode parameters of non-identical microstrip coupled lines. The computed values of mode velocities and mode impedances are compared with available results from the literature and experimental results on nonidentical microstrip couplers to test the applicability of the empirical relations.     

Scattering matrix of dielectric resonator coupled with twomicrostrip lines

A lumped equivalent circuit is proposed to model the coupling of a dielectric resonator with two microstrip lines terminated by any impedance. A three-dimensional finite-element method is used to determine the resonant frequency, quality factor, and coupling coefficients as functions of the electromagnetic parameters of the structure. Scattering parameters are computed. Methods are presented to evaluate these coefficients from a field analysis. They are shown to give good agreement between computed and experimental results     

Reflection coefficients of oversized coupling holes

Very simple analytical expressions are proposed for the reflection coefficients of coupling holes used in FIR waveguide lasers. The relations are carried out for dielectric and metallic circular waveguides.     

Design of grating-assisted waveguide couplers with weightedcoupling

The design of grating-assisted, channel waveguide codirectional couplers is demonstrated using the Gel'fand-Levitan-Marchenko inverse scattering method. Weighted coupling coefficients are computed from rational expression for the desired wavelength response. Approximate formulas that relate the waveguide and grating geometries to the computed coupling coefficients are derived. The technique is illustrated by designing a directional coupler with a third-order Butterworth filter characteristic and a 130 Å full-width-half-maximum bandwidth     

Propagation and optical interaction of guided acoustic waves intwo-mode optical fibers

Acoustic modes propagating in cylindrical solid rods are considered. A review of the properties of several mode groups is given, and computed results are shown for a wide range of material properties. The lower mode of each group is relevant for an all-fiber-optic frequency shifter recently demonstrated. For these modes, dispersion relations, mode patterns, power relations, and acoustooptic coupling strength are calculated. Some experimental results are compared with the calculations, and alterations to improve the frequency shifter are proposed     

熔锥型单模光纤耦合器模型的优化研究

在弱导和弱耦合近似条件下,对光纤耦合器的几何形状做近似处理,并采用连续函数进行描述.根据Snyderd的局部模式理论,采用三角波与高斯波的变系数叠加函数对光纤耦合器纵向各区域的光模场分布进行描述.利用局部模耦合理论和变分法计算分析光纤耦合器纵向各区域的传播常数和耦合系数,讨论耦合系数与结构参数和波长的关系.计算表明:光纤耦合器熔锥区对光纤耦合器中的光功率耦合行为的影响不可忽略,光纤纤芯半径和包层半径对耦合区和熔锥区的耦合系数的影响成相反趋势.因此,可以通过合理控制耦合器的结构参数,制作出宽带平坦光纤耦合器.     

A Complete Solution of the Inductive Iris with TE/sub k0/ Incidence in Rectangular Waveguide

A TE/sub k0/ wave incident on an inductive metal iris in a rectangular waveguide excites a reflected and a transmitted wave in the TE/sub k0/ mode. The reflection and transmission coefficients describing these waves are computed. In addition to the incident mode, a number of other modes are excited by the discontinuity. The amount of coupIing to these other modes, given by coupling coefficients, is determined using the variational technique. The method developed makes it possible to find the coupling to any desired mode without first finding the coupling to any other mode or group of modes. The analysis shows under what conditions certain modes can be suppressed or eliminated. The method should be applicable to other problems of interest where modes other than the incident one are excited. Since the reflection, transmission, and coupling coefficients are known, the total field at any point in the waveguide can be computed. As an example, the total field at the discontinuity when the TE/sub 10/ mode is incident is calculated. The result closely resembles the expected result (of zero electric field over the metal iris).     

基于小波系数关系的半脆弱水印方案

提出了基于小波变换系数间关系的半脆弱水印方案，通过构建小波域相邻及相应系数间的关系进行水印嵌入和提取，从而能够在侦测到对图像的恶意篡改的同时，对常见的图像处理仍保持很好的鲁棒性，此外由于对整个系数链进行了关联，所以系统的安全性在原有密匙保护的基础上又有大的提升。     

Accurate Analysis of Tapered Planar Transmission Lines for Microwave Integrated Circuits

A broad class of nonuniform transmission lines is analyzed through the method of coupled modes accompanied by the spectral domain solution of uniform lines. This combination offers efficient computation of the coupling coefficients. Small coupling allows the rigorous field theory of the spectral domain approach to give explicitly the scattering matrix of the taper. Several structures, including microstrip to coplanar waveguide taper and waveguide to fin-line taper, are successfully analyzed. The computed values of reflection coefficients are compared with the values derived by a simple impedance method and with the measured values. Results from the experimentally investigated tapers show that the theory is in good agreement.     

Exact calculations of scattering parameters of a step slot width discontinuity in a unilateral fin-line

The dominant and the first four higher-order modes in a unilateral fin-line are accurately described from a thorough spectral-domain approach. Then, coupling coefficients between eigenmodes at a step slot width discontinuity to be used in the generalised scattering matrix formulation are directly computed in the spectral domain. Scattering parameters of the dominant mode in the Ka band are presented.     

A direct method to compute the coupling between nonidentical microwave cavities

A new technique to compute the coupling, as a function of frequency, between nonidentical resonators is presented in this paper. The structure is separated by introducing electric and magnetic wall boundary conditions on the plane of separation, and coupling coefficient is computed directly from the eigenvalues of the four individual structures. The proposed technique has been used to compute the coupling between coaxial combline resonators. It is found to be computationally much faster than the iterative technique. The computed results are in good agreement with the measured results.     

Time domain analysis of transient propagation in inhomogeneous magnetized plasma using Z-transforms

The electromagnetic propagation through an inhomogeneous magnetized plasma slab is studied using the Z-transform formulation of the Finite-Difference Time-Domain（FDTD） method. The direction of electromagnetic propagation is parallel to the biasing magnetic filed. To validate the Z-transform algorithm, the reflection and transmission coefficients for the right-hand circularly polarized wave of the homogeneous magnetized plasma slab are computed by means of discrete Fourier transform. The comparison between the reflection and transmission coefficients of the homogeneous plasma slab and analytical values indicates that Z-transform algorithm is very accurate. When the plasma frequency varies according to the square root and parabolic relations, the reflection and transmission coefficients of the inhomogeneous magnetized plasma slab are computed.     

A coupled-mode theory for multiwaveguide systems satisfying the reciprocity theorem and power conservation

Two sets of coupled-mode equations for multiwaveguide systems are derived using a generalized reciprocity relation; one set for a lossless system and the other for a general lossy or lossless system. The second set of equations also reduces to those of the first set in the lossless case under the condition that the transverse field components are chosen to be real. Analytical relations between the coupling coefficients are shown and applied to the coupling of mode equations. It is shown analytically that our results satisfy exactly both the reciprocity theorem and power conservation. New orthogonal relations between the supermodes are derived in matrix form with the overlap integrals taken into account.     

Coupling coefficients of step-impedance resonators in stripeline band-pass filters of array type

There are researched specificities of electromagnetic coupling coefficients at main and higher resonance frequencies between step-impedance resonators, fabricated from symmetric stripe transmission lines with open ends. It is shown, modification of step resonators parameters can result in modification of the coupling coefficient at main resonance frequency in wide range, that allows to realize band-pass filters of array type. It is stated in case of several values of parameters of stripe resonators their coupling coefficients values at frequencies higher than main one are zero. It is proposed a new method of expansion of suppressed frequency band of pass-band filters of array type, which is based on suppression of the first parasitic pass band due to zero coupling coefficient.     

Coupling parameters for a side-coupled ring resonator and amicrostrip line

A ring resonator side coupled to a microstrip line shows two close but distinct resonance peaks. These are identified as due to even-mode (magnetic field) and odd-mode (electric field) coupling. Equivalent circuit models for both cases have been proposed and coupling parameters are calculated using piecewise, coupled-line approximations. The calculated coupling coefficients for the two cases are compared with the experimentally-measured coupling coefficients and show very good agreement with the models used     

Design of digital differentiators for low frequencies

Optimal, maximally accurate digital differentiators (DDS) are derived for the low-frequency range. Exact coefficients used in the proposed DDs can be readily computed from explicit formulas, whereas the optimal (minimas RE) DDs require and optimization program to derive the coefficients. The lower the frequency of differentiation, the better is the performance of the proposed differentiators, making them suitable for many typical applications     

Coupled modes of anisotropic polarization maintaining fibers

Wave coupling between the fundamental vector modal fields of two identical, polarization-maintaining, weakly guiding fibers is analyzed. An improved coupled-mode theory is used that also applies to anisotropic materials. Coupling coefficients that are the elements of a coupling matrix are calculated and presented as functions of the relative tilt angle between the two fiber principal axes. Exact analytical expressions for the eigenvalues and their associated eigenvectors are given in terms of the elements of this coupling matrix, for any relative tilt angle. Symmetry relations that are found between elements of the coupling matrix much simplify the presentation of the eigenvectors. A weak-coupling approximation of the eigenvector expressions, which is also given, retains their qualitative properties     

Derivation of parameters of Y-Z power-law relation from raindrop size distribution measurements and its application in the calculation of rain attenuation from radar reflectivity factor measurements

The work reported herein empirically derived the coefficients of the power-law relation between the specific attenuation Y and each of two other quantities: the radar reflectivity factor Z and the rainfall rate R. The derivation was accomplished using raindrop size distributions (DSDs) measured in Montreal and Toronto using the precipitation occurrence sensor system (POSS) and a Joss-Waldvogel disdrometer (JWD). The specific attenuation was calculated for both spherical and oblate spheroidal raindrops. Prior to doing so, the effects of inaccuracies in small drop detection by the two systems on the resulting Y-Z and Y-R relations were examined. In computing the relations, the influence of grouping the DSDs according to the corresponding values of Z was assessed. The results from the two sites were then combined in a regression analysis to determine the coefficients of the power-law expressions. The final expressions were used to calculate the probability distribution of rain attenuation over several path lengths at 30 GHz. Conclusions that can be drawn from this work include that (i) the uncertainties in the measurements of small drops do not appear to be critical to the derived relations for some frequencies considered in this work, (ii) in computing rain attenuation estimates from radar reflectivity factors, different criteria for grouping the reflectivity factor measurements can be adopted without changing the statistics of the corresponding attenuation estimates, (iii) differences, which are the smallest for frequencies around 20-30 GHz, are observed in the coefficients derived from the measured DSDs compared with those recommended by the ITU-R, and (iv) the attenuation statistics at 30 GHz computed by applying the Y-Z power-law expression are resistant to spatial averaging.     

Ray-Optical Calculation of Edge Diffraction in Unstable Resonators

A previously developed ray-optical theory for calculation of modal reflection and coupling coefficients due to edge discontinuities in homogeneously or inhomogeneously filled parallel-plane waveguides is generalized to waveguides with nonplanar boundaries. Treated in particular are the reflections from the open ends of a bilaterally truncated waveguide whose convex walls are confocal hyperbolas. This open configuration serves as a model for unstable optical resonators with cylindrical mirrors. The ray optically determined modal reflection and coupling coefficients for mirrors with large Fresnel number are shown to reduce to those in a previously employed local parallel-plane approximation when the Fresnel numbers are moderate. The analysis quantifies proposed ray-optical models for explaining the influence of edge diffraction on the behavior of the resonant modes.     

Theoretical of and Experimental Investigation Finline Discontinuities

The dominant and the first-five higher order modes in a unilateral finline are precisely described from a thorough spectral-domain approach. Then, using the modal analysis, coupling coefficients between eigenmodes at a discontinuity that have to be introduced into the scattering matrix formulation are directly computed in the spectral-domain, and, consequently, the equivalent circuit parameters of the discontinuity are determined. Finafly, finline discontinuities often used for impedance transformation are investigated and a good agreement between theoretical and experimental results is reported.